Time discrete filter comprising upsampling, sampling rate conversion and downsampling stages
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 US7376690B2 US7376690B2 US10495583 US49558304A US7376690B2 US 7376690 B2 US7376690 B2 US 7376690B2 US 10495583 US10495583 US 10495583 US 49558304 A US49558304 A US 49558304A US 7376690 B2 US7376690 B2 US 7376690B2
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 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
 H03H17/00—Networks using digital techniques
 H03H17/02—Frequency selective networks
 H03H17/0248—Filters characterised by a particular frequency response or filtering method
 H03H17/0264—Filter sets with mutual related characteristics
 H03H17/0273—Polyphase filters
 H03H17/0275—Polyphase filters comprising nonrecursive filters
 H03H17/0276—Polyphase filters comprising nonrecursive filters having two phases

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
 H03H17/00—Networks using digital techniques
 H03H17/02—Frequency selective networks
 H03H17/04—Recursive filters
 H03H17/0416—Recursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing
 H03H17/0427—Recursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies
 H03H17/0438—Recursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies the ratio being integer
 H03H17/045—Recursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies the ratio being integer where the outputdelivery frequency is lower than the input sampling frequency, i.e. decimation

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
 H03H17/00—Networks using digital techniques
 H03H17/02—Frequency selective networks
 H03H17/06—Nonrecursive filters
 H03H17/0621—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing
 H03H17/0635—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies
 H03H17/065—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies the ratio being integer
 H03H17/0657—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies the ratio being integer where the outputdelivery frequency is higher than the input sampling frequency, i.e. interpolation

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
 H03H17/00—Networks using digital techniques
 H03H17/02—Frequency selective networks
 H03H17/06—Nonrecursive filters
 H03H17/0621—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing
 H03H17/0635—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies
 H03H17/065—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies the ratio being integer
 H03H17/0664—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies the ratio being integer where the outputdelivery frequency is lower than the input sampling frequency, i.e. decimation

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
 H03H17/00—Networks using digital techniques
 H03H17/02—Frequency selective networks
 H03H17/06—Nonrecursive filters
 H03H17/0621—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing
 H03H17/0635—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies
 H03H17/0685—Nonrecursive filters with inputsampling frequency and outputdelivery frequency which differ, e.g. extrapolation; Antialiasing characterized by the ratio between the inputsampling and outputdelivery frequencies the ratio being rational

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
 H03H17/00—Networks using digital techniques
 H03H17/02—Frequency selective networks
 H03H17/0283—Filters characterised by the filter structure
 H03H17/0286—Combinations of filter structures
 H03H17/0288—Recursive, nonrecursive, ladder, lattice structures
Abstract
Description
The present invention relates to a time discrete filter, comprising a sampling rate converter provided with an input and an output, and a downsampler having a downsampling factor n_{d}.
The present invention also relates to a communication device comprising such a time discrete filter and to a method, wherein a sampling rate of an input signal is converted with a factor m.
Such a time discrete filter is known from WO 99/38257. The known time discrete filter comprises a cascade arrangement of sampling rate converters, exemplified by respective downsamplers alternated by filter sections in order to require less computational resources in the time discrete filter. Disadvantage is however the comprehensive and complex hardware and software required for the known time discrete filter.
Therefore it is an object of the present invention to provide an improved time discrete filter, whose complexity in terms of required amount of multiplications, additions, as well as storage requirements is reduced.
Thereto the time discrete filter according to the invention is characterised in that it further comprises an upsampler having an upsampling factor n_{u}, that the upsampler is coupled to the converter input, and that the converter output is coupled to the downsampler.
Consequently the method according to the invention is characterised in that the input signal is first upsampled with a factor n_{u}, then subjected to the sampling rate conversion with the factor m and finally downsampled with a factor n_{d}.
Surprisingly it has been found that if a sampling rate conversion operation is preceded by an upsampling operation and only after the conversion is followed by a downsampling operation to a wanted sampling frequency, that then the complexity in terms of the ultimate number of calculations, in particular multiplications and additions, necessary in the filter according to the invention is reduced. This leads to a decrease of the number of instructions per second which is a measure for the complexity of a Digital Signal Processing (DSP) algorithm. In addition this leads to an associated decrease of power consumed by DSP in said filter, such as applied in for example audio, video, and (tele)communication devices, as well as radio and television apparatus.
An embodiment of the time discrete filter according to the invention is characterised in that the sampling rate converter is capable of performing decimation or interpolation.
The above advantages hold irrespective whether decimation or interpolation is applied in the filter according to the invention.
A further embodiment of the time discrete filter according to the invention is characterised in that the sampling rate converter has a sampling rate conversion factor m, where m is an integer larger than 2.
Advantageously any sampling rate factor, such as 3, 5, 7 or for example 125, such as necessary in GSM and Bluetooth systems can be used. Preferably prime numbers or a combination of prime numbers are used as sampling rate conversion factors, which normally give rise to a more complicated filter configuration.
A still further embodiment of the time discrete filter according to the invention is characterised in that the upsampling factor n_{u }and the downsampling factor n_{d }each are larger or equal to 2.
If the upsampling factor n_{u }and/or the downsampling factor n_{d }are 2, the total complexity is reduced considerably due to the fact that the resulting filter structures are more efficient. If properly implemented such as with FIR and/or IIR filter configurations, also the number of delay elements and the amount of storage required for the data samples and the coefficients in the filter according to the invention decreases, resulting in additional cost savings.
At present the time discrete filter and method according to the invention will be elucidated further together with their additional advantages, while reference is being made to the appended drawing, wherein similar components are being referred to by means of the same reference numerals. In the drawing:
By way of example
If one stage downsampling according to
Table I hereunder gives the complexity in terms of the necessary number of multiplications and additions, and the data sample and coefficient storage capacity required in the one stage filter of
TABLE I  
Number of  FIR implementation  IIR implementation  
Multiplications  20.8 * F_{s}  7 * F_{s}  
Additions  22.8 * F_{s}  15 * F_{s}  
Data samples  22  10  
Coefficients  58  7  
Filter sections 6 and 11 having transfer functions H1(z) and H2(z) respectively can each be implemented digitally by a Finite Impulse Response (FIR) filter and/or an Infinite Impulse Response (IIR) filter. Examples thereof will be given hereinafter.
 (a) three input samples at the upper, middle and lower horizontal parallel lines 1 _{1}, 1 _{3}, 1 _{5 }respectively coupled to the switch S_{1 }and zeros at the other two lines 1 _{2 }and 1 _{4 }respectively, or
 (b) zeros at the upper, middle and lower lines 1 _{1}, 1 _{3}, 1 _{5 }respectively and two input samples at the other two lines 1 _{2 }and 1 _{4 }respectively.
In case (a) this amounts to 4+2+4=10 multiplications and 2+3+3=11 additions and in case (b) this amounts to 1+3*2=7 additions. So 18 multiplications and 18 additions are needed for 5 input samples; equivalent with a rate F_{s}/5. Also 3 data samples and 10 coefficients need to be stored. See table II hereunder.
If use is made of a IIR filter for configuring the transfer function H1(z) of
TABLE II  
Number of  FIR case  IIR case  
Multiplications  3.6F_{s}  10F_{s}  
Additions  3.6F_{s}  17F_{s}  
Data samples  3  8  
Coefficients  10  5  
It follows from table II that the FIR case is more efficient than the IIR case. This is due to the fact that the polyphase decomposition can be used for the FIR case, but not for the IIR case. The minor disadvantage for the FIR case is that twice the number of coefficients have to be stored. Therefore hereafter only the FIR case will be used for implementing H1(z).
Next the filter design of the transfer function H2(z) of
TABLE III  
One stage  Two stage  
Number of  FIR  FIR H1(z)  FIR H2(z)  FIR total 
Multiplications  20.8F_{s}  3.6F_{s}  4.8F_{s}  8.4F_{s} 
Additions  22.8F_{s}  3.6F_{s}  9.2F_{s}  12.8F_{s} 
Data samples  22  3  23  26 
Coefficients  58  10  24  34 
From table III it can be concluded that a two stage FIR filter is more efficient than a one stage FIR filter. Only the number of data samples to be stored is higher in the two stage FIR filter.
A very efficient filter structure is the two stage configuration having a FIR structure for the H1(z) filter explained above and an IIR structure for the H2(z) filter of
TABLE IV  
One stage  Two stage  
Number of  IIR  FIR H1(z)  IIR H2(z)  FIR & IIR total 
Multiplications  7F_{s}  3.6F_{s}  0.8F_{s}  4.4F_{s} 
Additions  15F_{s}  3.6F_{s}  1.8F_{s}  5.4F_{s} 
Data samples  10  3  7  10 
Coefficients  7  10  4  14 
It may be again be concluded that the two stage FIR & IIR solution is more efficient than the one stage IIR solution in terms of number of required multiplications and additions. Only somewhat more filter coefficients have to be stored.
The above explained filter concepts may of course be generalised to other generally prime down sampling or up sampling factors. The corresponding structures for up sampling by a prime number or product thereof larger than 2 can be found by using the well known transposition theorem. See “On the Transposition of Linear TimeVarying DiscreteTime Networks and its Applications to Multirate Digital Systems” by T. A. C. M. Claasen and W. F. G. Mecklenbräuker, Philips Journal of Research, 1978, pp 78102.
The filter concepts explained above may be applied in any digital transmission or communication system or device. Examples thereof are digital data processing devices or filters, telephone sets, audio or video processing devices, television, image processing devices or the like. The filter 4 may be implemented in a way known per se by for example a switched capacitor filter or a switched current filter.
Whilst the above has been described with reference to essentially preferred embodiments and best possible modes it will be understood that these embodiments are by no means to be construed as limiting examples of the circuits and methods concerned, because various modifications, features and combination of features falling within the scope of the appended claims are now within reach of the skilled person.
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DE102009008092B4 (en) *  20090209  20141030  Atlas Elektronik Gmbh  Method and apparatus for compensating for variations in sample 
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